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Classification of exact solutions for some nonlinear partial differential equations with generalized evolution. (English) Zbl 1247.35124

Summary: We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa-Holm-KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.

MSC:

35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35C11 Polynomial solutions to PDEs

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